Jim is building a deck for his family to enjoy. Because of a big bay window that juts out next to the deck, he has to build an angled section for the steps going down to the yard. The section will be a parallelogram. Assuming that he cannot accurately prove that any two sides are parallel, how can he be assured that he has an actual parallelogram? Identify the theorem that he will use and how he will use it

Answer:

\(-\frac{5}{3}\)

Step-by-step explanation:

\(m (slope)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

\(m=\frac{-1-(-6)}{5-8}\)

\(m=-\frac{5}{3}\)

Answer: After 1 year:    $5,610

After 2 years: $5,722.20

Step-by-step explanation: Use the formula for periodic compounding interest, which is

A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the interest rate as a decimal, n is the number of times the interest is compounded per year, and t is how many years.

Here, P = 5,500, r = 0.02  (that's 2% as a decimal), n = 1,

t = 1 for the first answer, t = 2 for the second answer (1 year, then for 2 years)

Plug the known values in to solve...

For 1 year...

A = 5,500(1 + 0.02/1)^(1*1)

  A = 5,500(1.02)^1

     A = 5,610

For 2 years...

A = 5,500(1 + 0.02/1)^(1*2)

  A = 5,500(1.02)²

     A = 5,722.20

Answer:  A=2 B=4 C=5

Step-by-step explanation:

After your grandmother makes a $5,000 deposit on your 18th birthday, the amount in the savings account can be calculated using compound interest. Assuming the account pays an interest rate of 7%, the amount in the account immediately after the deposit can be determined by applying the compound interest formula.

To calculate the amount in the savings account after the deposit on your 18th birthday, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A represents the final amount, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $5,000, the interest rate is 7% (or 0.07 as a decimal), and the deposit is made on your 18th birthday, which means the time is 17 years. Since no information is given about the compounding frequency, let's assume it is compounded annually (n = 1).

Plugging in the values into the compound interest formula, we have A = 5000(1 + 0.07/1)^(1*17) = 5000(1.07)^17 ≈ $15,128.

Therefore, the amount in the savings account immediately after your grandmother makes the deposit on your 18th birthday is approximately $15,128, rounded to the nearest dollar.

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The covariance matrix of Y is given by

Cov (Y) =  

      [[1, 1, 0],

       [1, 2, 1],

       [0, 1, 2]]

The joint PDF of Y can be obtained as

fY(y1,y2,y3) = (1/√(2π))^3  * exp ( -1/2 * [y1^2 + y2^2 + y3^2 - 2y1y2 - 4y2y3 - 2y1y3])

The joint PDFs of Yi and Y2, Yi and Y3 and Y2 and Y3 are given by:

fY1Y2(y1,y2) = (1/√(2π))^2 * exp(-1/2 * (y1^2 + y2^2 - 2y1y2))

fY1Y3(y1,y3) = (1/√(2π))^2 * exp(-1/2 * (y1^2 + y3^2 - 2y1y3 - 4y2y3))

fY2Y3(y2,y3) = (1/√(2π))^2 * exp(-1/2 * (y2^2 + y3^2 - 4y2y3))

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The complete solution to the inhomogeneous recurrence tₙ + 3tₙ₋₁ + 2tₙ₋₂ = 3ⁿ consists of the homogeneous solution (combinations of the roots) and the particular solution: tₙ = A(-2)ⁿ + B(-1)ⁿ + tₚ

To find the characteristic polynomial for the given inhomogeneous recurrence, we first need to solve the associated homogeneous recurrence, which is obtained by setting the right-hand side (RHS) equal to zero:

tₙ + 3tₙ₋₁ + 2tₙ₋₂ = 0

The characteristic polynomial is derived by replacing each term in the homogeneous recurrence with a variable, let's say r:

r² + 3r + 2 = 0

Now we can solve this quadratic equation to find the roots:

(r + 2)(r + 1) = 0

This equation has two roots:

r₁ = -2

r₂ = -1

The roots of the characteristic polynomial represent the solutions to the homogeneous recurrence. Since the equation is second-order, there are two distinct roots.

Next, we need to consider the inhomogeneous part of the recurrence, which is 3ⁿ. The inhomogeneous part does not affect the roots of the characteristic polynomial but instead contributes to the particular solution.

Since the inhomogeneous part can be parsed as 1 * 3ⁿ, we have p(n) = 1 and b = 3.

The characteristic polynomial remains unchanged:

(r + 2)(r + 1) = 0

The roots of the characteristic polynomial are:

r₁ = -2 (with multiplicity 1)

r₂ = -1 (with multiplicity 1)

These roots represent the solutions to the homogeneous recurrence.

To find the particular solution, we use the fact that b/p(n) = 3/1 = 3. Since p(n) = 1, the particular solution is a constant, which we can denote as tₚ.

Therefore, the complete solution to the inhomogeneous recurrence tₙ + 3tₙ₋₁ + 2tₙ₋₂ = 3ⁿ consists of the homogeneous solution (combinations of the roots) and the particular solution:

tₙ = A(-2)ⁿ + B(-1)ⁿ + tₚ

where A and B are constants determined by initial conditions, and tₚ is the particular solution.

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The values of the coefficients and constant in the quadratic function are a = 1, b = -5, and c = 6, where a and b are coefficients and c is the constant.

Given quadratic function f(x) = x² - 5x + 6.

The values of the coefficients and constant in the function are

a = 1

b = -5

c = 6

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Step-by-step explanation:

l = 3 + 2w

P= 2w t 2l

= 2w+2(3+2w)

=2w+6+4w

=6w+6 = 54

6w=48

w=8

divide 6 both side

l=3+2(8)=3+16=19

answer

width 8feet and length 19 feet

What is your question dude???????

Based on both the p-value method and the critical value method, we fail to reject the null hypothesis and cannot infer that the two groups differ in the mean number of pictures printed.

To determine if the two groups (digital camera owners and standard camera owners) differ in the mean number of pictures printed, we can conduct a hypothesis test using both the p-value method and the critical value method.

Let's define our hypotheses:

Null Hypothesis (\(H_0\)): The mean number of pictures printed is the same for both groups.

Alternative Hypothesis (\(H_1\)): The mean number of pictures printed differs between the two groups.

We'll use a significance level of 0.05 (5%).

First, let's calculate the test statistic for the two-sample t-test using the provided summary statistics:

Digital:

Mean = 18.25

Standard Deviation = 6.5

Sample Size = 8

Standard:

Mean = 16.5

Standard Deviation = 19.2

Sample Size = 8

Using the formula for the two-sample t-test, the test statistic (t) is given by:

\(t = (mean_1 - mean_2) / \sqrt{(s_1^2/n_1) + (s_2^2/n_2)}\)

Substituting the values, we have:

\(t = (18.25 - 16.5) / \sqrt{(6.5^2/8) + (19.2^2/8)}\)

t ≈ 0.75

Now, let's perform the hypothesis test using both methods:

1) P-value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom, we can calculate the p-value associated with the test statistic.

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Using a t-table or statistical software, we find that the p-value corresponding to t ≈ 0.75 is approximately 0.47.

Since the p-value (0.47) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

2) Critical Value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom and a significance level of 0.05, we can find the critical value.

The critical value is the value beyond which we would reject the null hypothesis.

For a two-tailed test at a 5% significance level and 14 degrees of freedom (8 + 8 - 2), the critical value is approximately ±2.145.

Since the test statistic (0.75) does not exceed the critical value (±2.145), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

In conclusion, based on both the p-value method and the critical value method, we do not have sufficient evidence to infer that the two groups differ in the mean number of pictures printed.

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Answer: y = x * 0.02

Step-by-step explanation:

When you multiply the number in x by 0.02 you end up with the product of y.

Answer:

y = x * 0.02

Step-by-step explanation:

Answer:

i think its 2x+1

Step-by-step explanation:

1 Split the second term in 2{x}^{2}-5x-32x  

2

−5x−3 into two terms.

2{x}^{2}+x-6x-3

2x  

2

+x−6x−3

2 Factor out common terms in the first two terms, then in the last two terms.

x(2x+1)-3(2x+1)

x(2x+1)−3(2x+1)

3 Factor out the common term 2x+12x+1.

(2x+1)(x-3)

(2x+1)(x−3)

Done

Answer:

C)2x+3

Step-by-step explanation:

just took the test

alegebra 2 (2019)

Answer:

442

Step-by-step explanation:

Answer:

a/e

~~~~~~~~~~

\(\frac{(18) ab (20)cd}{ (15) bc (24) de}\)

\(\frac{(3) ab (4)cd}{ (3) bc (4) de}\\\)

\(\frac{ ab cd}{ bc de}\\\)

\(\frac{ a }{ e}\\\)

Step-by-step explanation:

Answer:

the circumstance is 31.42

Answer:

$10

Step-by-step explanation:

6x-15=45

+15. +15

6x=60

/6. /6

x=10

Answer:

$7.5¢ or \(7\frac{1}{2}\)

Step-by-step explanation:

Do not use This solution:

Firstly, lets find how much the hats cost initially before the 15% coupon. To do that, divide, not multiply, divide $45 by 15% because 15% off means multiply 15% from the original price. But in this case we need to find the initial amount before the 15% coupon.

15% = \(\frac{15}{100}\)

Now, set it up;

\(\frac{15}{100}\) ×\(\frac{45}{1}\)

45 ÷ 6 = 7.5

The expected raise a union wage negotiator feels that   the union members will get is $1.22.

The probability of each pay raise is given below

P ($1.50 raise) = 0.40

P ($1.00 raise) = 0.30

P ($0.50 raise) = 0.20

P (no raise) = 0.10

The probability of each pay raise is then multiplied by the pay itself

Expected raise for each hour = $1.50(0.40) + $1.00(0.30) + $0.50(0.20) + $0.00(0.10)

E(x) = 0.6 + 0.52 + 0.1 + 0 (The probability of no pay at all gives 0 since the pay amount has no value)

E(x) = $1.22

Therefore, all together the union wage negotiator is able to predict a $1.22 pay raise for the workers for each time expected.

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Answer:

is this correct

Step-by-step explanation:

(c+b)=d/a

c=d/a -b

The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.

To solve this problem, we can use the concept of probability and the binomial distribution.

The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.

The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.

The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.

The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).

So, the probability of at least one defective rivet is:

P(at least one defective rivet) = 1 - P(no defective rivets)

P(at least one defective rivet) = 1 - (1 - p)^27

Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.

For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:

P(at least one defective rivet) = 1 - (1 - 0.05)^27

P(at least one defective rivet) ≈ 0.683

Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.

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Answer:

21

Step-by-step explanation:

It landed on 4 and 5 about 37% of the time with 240 rolls. So since 60 is 1/4 of 240, we just divided the number of times it landed on 4 and 5 by 4. So since it landed on 4 or 5 84 times, we divide 84 by 4

84 ÷ 4 = 21

So the number of times the cube will land on 4 or 5 is 21

Answer:

y = 2.5x

Step-by-step explanation:

The equation representing direct proportion is

y = kx ← k is the constant of proportion

Here k = 2.5 , thus

y = 2.5x ← equation of proportion

Answer:

A

Step-by-step explanation:

what the other guy said

Answer:

Step-by-step explanation:

If I found the mean, the answer would be:

3+ 4+4+4+5+6+7+23= 56

56/ 8 = 7

If I found the average value using the median, the answer would be 4.5.

In this set of data, the anomaly is 23 as it is much higher than the other numbers.

The median is more accurate because it find the more ‘central’ number and is not affected as greatly with anomalies whereas the mean is affected greatly with anomalies as it raises the value significantly.

Therefore, the median is better to work out the average in this set of data.

:)

The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:

f(x) = 1 / (b - a)

where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.

To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.

Therefore, the probability that the commuting time will be between 50 and 60 minutes is:

P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.

Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.

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We can write the inequality involving absolute value to express the statement as:

|x - 52| ≤ 39  Where x is the temperature in degrees Fahrenheit.

The inequality involving absolute value to express the statements are:

A. The weatherman predicted that the temperature would be within 39 of 52°F.

We can write the inequality involving absolute value to express the statement as:

|x - 52| ≤ 39

Where x is the temperature in degrees Fahrenheit.

This absolute value inequality states that the temperature should be within 39°F of 52°F. Hence, the temperature can be 13°F or 91°F. However, if the temperature goes beyond these limits, then it is not within 39 of 52°F.B. Serena will make the B team if she scores within 8 points of the team average of 92.

We can write the inequality involving absolute value to express the statement as:

|x - 92| ≤ 8

Where x is the score obtained by Serena. This absolute value inequality states that the score obtained by Serena should be within 8 points of the team average of 92. Hence, if the average score is 92, then Serena can score between 84 and 100. However, if Serena's score goes beyond these limits, then she will not make it to the B team.

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Answer:

6) 10,4,-2,-8

7) 5,10,15,20

8) 1,7,13,18

Step-by-step explanation:

that is the answr

The distance from the bird to the top of the tree is 61.95 feet.

We have,

Angle of elevation to the top of the tree: 38 degrees.

Angle of elevation to the bird: 60 degrees.

Distance from the base of the tree to your position: 84 feet.

Let the distance from the bird to the top of the tree as 'x'.

Using Trigonometry

tan(38) = height of the tree / 84

height of the tree = tan(38) x 84

and, tan(60) = height of the tree / x

x = height of the tree / tan(60)

Substituting the value of the height of the tree we obtained earlier:

x = (tan(38) x 84) / tan(60)

x ≈ 61.95 feet

Therefore, the distance from the bird to the top of the tree is 61.95 feet.

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